Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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MINIMAL POLYNOMIAL DYNAMICS ON THE p-ADIC INTEGERS

  • Sangtae Jeong (Department of Mathematics Inha University)
  • Received : 2021.08.13
  • Accepted : 2022.05.13
  • Published : 2023.01.01
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Abstract

In this paper, we present a method of characterizing minimal polynomials on the ring 𝐙p of p-adic integers in terms of their coefficients for an arbitrary prime p. We first revisit and provide alternative proofs of the known minimality criteria given by Larin [11] for p = 2 and Durand and Paccaut [6] for p = 3, and then we show that for any prime p ≥ 5, the proposed method enables us to classify all possible minimal polynomials on 𝐙p in terms of their coefficients, provided that two prescribed prerequisites for minimality are satisfied.

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Acknowledgement

This work was conceived from a question of F. Durand while I was participating in the workshop on 2019 Numeration and Substitution, which was held in the Erwin Schrodinger International Institute for Mathematics and Physics. I would like to thank him for his question and interest in my early work. I would also like to express gratitude to the referee for some suggestions, which improve the paper for clearer understanding.

References

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